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Parker, RL, Gee JS.  2002.  Calibration of the pass-through magnetometer - II. Application. Geophysical Journal International. 150:140-152.   10.1046/j.1365-246X.2002.01692.x   AbstractWebsite

We describe the experimental procedure we use to calibrate a cryogenic pass-through magnetometer. The procedure is designed to characterize the magnetometer sensitivity as a function of position within the sensing region. Then we extend a theory developed in an earlier paper to cover inexact observations and apply it to the data set. The theory allows the calculation of a smooth, harmonic, internally consistent interpolating function for each of the nine components of the response tensor of the magnetometer. With these functions we can calculate the response to a dipole source in any orientation and position, and predict the magnetometer signal from any kind of specimen. The magnetometer in the paleomagnetic laboratory onboard the research vessel Joides Resolution is the subject of one such experiment and we present the results. The variation with position of sensitivity is displayed in a series of plane slices through the magnetometer. We discover from the calibration model that the X and Z coils are misaligned so that the magnetic centre of the coils is displaced from the geometric centre by approximately 0.7 cm. We synthesize the signal expected from the magnetometer when a variety of simple cores are measured. We find that, unless appropriate corrections are made, changes in magnetization direction can appear as variations in magnetic intensity, and conversely, fluctuations in the magnetization strength can produce apparent swings in declination and inclination. The magnitude of these effects is not small and is certainly worth taking into account in the interpretation of records from this kind of instrument. In a pilot study on data from a core measured with the shipboard magnetometer, we observe some large distortions, particularly in declination, that are attributable to uncorrected instrumental effects.

Parker, RL.  2000.  Calibration of the pass-through magnetometer—I. Theory. Geophysical Journal International. 142:371-383.   10.1046/j.1365-246x.2000.00171.x   AbstractWebsite

By studying a simple model of a pass-through magnetometer we show that there are circumstances in which misleading results might arise if the spatial sensitivity of the instrument is not properly corrected. For example, if the core sample is not correctly centred, or the magnetometer itself is misaligned, serious distortion can appear in the inferred inclination distribution. The possibility of such errors warrants a thorough study of laboratory instruments and, as a first step, we require a spatial calibration, that is, an estimate of the sensitivity of the various coils to samples placed anywhere in the sensing region. Only when this information is available for laboratory magnetometers will it be possible to calculate suitable corrections. The fact that laboratory magnetometers employ superconducting material makes inferring the response from the geometry of the coils impractical because the field from a specimen is modified inside the instrument by image currents flowing in the superconducting elements. To overcome this obstacle we treat a very general calibration problem. We show that the sensitivity of a particular coil as a function of position obeys Laplace's equation, and therefore the description in space of the sensitivity is mathematically exactly the same as modelling the geomagnetic field. A calibration experiment consists of several hundred measurements performed on a tiny dipole sample, systematically positioned throughout the sensing volume of the instrument. From such observations we aim to construct a harmonic interpolating function that represents the response in the measurement region. The natural geometry for the problem is that of a cylinder, so we work from the cylindrical harmonic expansion of an equivalent magnetic field. Cylindrical harmonic expansions take the form of an infinite set of unknown functions, not just a collection of coefficients as with spherical harmonics. To build a suitable interpolating function from them we appeal to the principles of spline interpolation by constructing a model that minimizes some measure of response complexity. We examine in detail two such measures. The first corresponds to magnetic field energy; the second is a more abstract norm that smoothes more heavily than the energy norm, and whose Gram matrix elements can be found without recourse to lengthy numerical procedures. The second norm promises to form the basis of a practical programme of calibration.

Parker, RL.  2010.  Can a 2-D MT frequency response always be interpreted as a 1-D response? Geophysical Journal International. 181:269-274.   10.1111/j.1365-246X.2010.04512.x   AbstractWebsite

Weidelt and Kaikkonen showed that in the transverse magnetic (TM) mode of magnetotellurics it is not always possible to match exactly the 2-D response at a single site with a 1-D model, although a good approximation usually seems possible. We give a new elementary example of this failure. We show for the first time that the transverse electric (TE) mode responses can also be impossible to match with a 1-D response, and that the deviations can be very large.

Parker, RL.  1997.  Coherence of signals from magnetometers on parallel paths. Journal of Geophysical Research-Solid Earth. 102:5111-5117.   10.1029/96jb03803   AbstractWebsite

During a recent marine magnetic survey of the Juan de Fuca Rise, two magnetometers were towed near the seafloor, one about 300 m above the other. To understand how to interpret the records, we investigate a simple statistical model: two magnetometers moving on parallel paths above a statistically stationary source, with known spectrum. Magnetometers on paths normal to perfectly lineated magnetic anomalies will measure signals that have unit coherence at all wavelengths. Departure of the system from this ideal state can be diagnosed by a; lower coherence, and something about the across-track structure can be learned from the shape of the coherence spectrum. We calculate the power and cross spectra of the profile signals in terms of the two-dimensional power spectrum of the field just above the source region; hence we obtain the coherence and phase spectra. For the special case of a white source spectrum we find surprisingly high coherences. A set of inequalities between the spectral estimates is derived and can be used to check the consistency of the measured signals with the model assumptions. The theory is applied to a magnetic traverse of the Juan de Fuca Rise when two near-bottom magnetometers were deployed. The key results are these: in the wavelength range above about 1 km the observed coherency is substantially higher than that from the disordered field model, consistent with the highly lineated structures observed at the surface over all ocean ridge systems. On scales between 500 m and 1 km the coherence falls to levels indistinguishable from those given by an isotropic flat spectrum, implying that on these scales there is little or no across-track lineation. This finding means that the resolution of paleomagnetic field behavior based on seafloor data in this area is no better than 36,000 years.

Prieto, GA, Thomson DJ, Vernon FL, Shearer PM, Parker RL.  2007.  Confidence intervals for earthquake source parameters. Geophysical Journal International. 168:1227-1234.   10.1111/j.1365-246X.2006.03257.x   AbstractWebsite

We develop a method to obtain confidence intervals of earthquake source parameters, such as stress drop, seismic moment and corner frequency, from single station measurements. We use the idea of jackknife variance combined with a multitaper spectrum estimation to obtain the confidence regions. The approximately independent spectral estimates provide an ideal case to perform jackknife analysis. Given the particular properties of the problem to solve for source parameters, including high dynamic range, non-negativity, non-linearity, etc., a log transformation is necessary before performing the jackknife analysis. We use a Student's t distribution after transformation to obtain accurate confidence intervals. Even without the distribution assumption, we can generate typical standard deviation confidence regions. We apply this approach to four earthquakes recorded at 1.5 and 2.9 km depth at Cajon Pass, California. It is necessary to propagate the errors from all unknowns to obtain reliable confidence regions. From the example, it is shown that a 50 per cent error in stress drop is not unrealistic, and even higher errors are expected if velocity structure and location errors are present. An extension to multiple station measurement is discussed.

Gill, AE, Parker RL.  1970.  Contours of “h cosec θ” for the world's oceans. Deep-Sea Research. 17:823-&.   10.1016/0011-7471(70)90044-6   AbstractWebsite

Contours of d = h cosec θ are presented for the worlds oceans, where h is the depth of the ocean and θ the latitude. This quantity is the distance between the ocean surface and the ocean floor in the direction of the axis of rotation of the earth. The inverse is proportional to 2Ω/d = f/h where Ω is the rate of rotation of the earth and f = 2Ω sinθ is the Coriolis parameter. The quantity f/h may be interpreted as the potential vorticity of the ocean in the absence of motion relative to the rotating earth.